Answer:
![Rate = 9(t+1)](https://tex.z-dn.net/?f=Rate%20%3D%209%28t%2B1%29)
Step-by-step explanation:
Given
![f(x) = 9x^2 - 2](https://tex.z-dn.net/?f=f%28x%29%20%3D%209x%5E2%20-%202)
![Interval = [1,t]](https://tex.z-dn.net/?f=Interval%20%3D%20%5B1%2Ct%5D)
Required
Determine the average rate of change
This is calculated using:
![Rate = \frac{f(b) - f(a)}{b - a}](https://tex.z-dn.net/?f=Rate%20%3D%20%5Cfrac%7Bf%28b%29%20-%20f%28a%29%7D%7Bb%20-%20a%7D)
Where
![[a,b] = [1,t]](https://tex.z-dn.net/?f=%5Ba%2Cb%5D%20%3D%20%5B1%2Ct%5D)
So, we have:
![Rate = \frac{f(t) - f(1)}{t - 1}](https://tex.z-dn.net/?f=Rate%20%3D%20%5Cfrac%7Bf%28t%29%20-%20f%281%29%7D%7Bt%20-%201%7D)
Solve for f(t) and f(1)
![f(t) = 9t^2 - 2](https://tex.z-dn.net/?f=f%28t%29%20%3D%209t%5E2%20-%202)
![f(1) = 9*1^2 - 2](https://tex.z-dn.net/?f=f%281%29%20%3D%209%2A1%5E2%20-%202)
![f(1) = 9 - 2](https://tex.z-dn.net/?f=f%281%29%20%3D%209%20-%202)
![f(1) = 7](https://tex.z-dn.net/?f=f%281%29%20%3D%207)
So, we have:
![Rate = \frac{9t^2 - 2 - 7}{t - 1}](https://tex.z-dn.net/?f=Rate%20%3D%20%5Cfrac%7B9t%5E2%20-%202%20-%207%7D%7Bt%20-%201%7D)
![Rate = \frac{9t^2 - 9}{t - 1}](https://tex.z-dn.net/?f=Rate%20%3D%20%5Cfrac%7B9t%5E2%20-%209%7D%7Bt%20-%201%7D)
Factorize:
![Rate = \frac{9(t^2 - 1)}{t - 1}](https://tex.z-dn.net/?f=Rate%20%3D%20%5Cfrac%7B9%28t%5E2%20-%201%29%7D%7Bt%20-%201%7D)
Apply difference of two squares
![Rate = \frac{9(t- 1)(t+1)}{t - 1}](https://tex.z-dn.net/?f=Rate%20%3D%20%5Cfrac%7B9%28t-%201%29%28t%2B1%29%7D%7Bt%20-%201%7D)
![Rate = 9(t+1)](https://tex.z-dn.net/?f=Rate%20%3D%209%28t%2B1%29)
Answer:
y = -4, x = -9
Step-by-step explanation:
System: -2x + 5y = -2, x - 3y = 3
Multiply the second equation: 2x - 6y = 6
Elimination:
-2x + 5y = -2
<u>+ 2x - 6y = 6</u>
- y = 4 --> y = - 4
Plug in: x - 3(-4) = 3
x + 12 = 3
x = -9
In order to find out the answer, we need to analyze the letters of the word MAGNETIC
there are 8 letters, all different
so it is 8!=1*2*3*4*5*6*7*8=4032 permutations <span />
Answer: b and d
Step-by-step explanation:
What are the measures of angles B and D? A. ∠B ... The perimeter of parallelogram ABCD is 46 inches. ... What is the measure of angle O in parallelogram LMNO? ... Consider the diagram and proof below. ... Rectangle PQRS is shown with its diagonals, PR and QS. ... Which equation can be used to find the measure of ?
Answer:
4in
Step-by-step explanation:
The width of the rectangle is
36:9=4